# [seqfan] Re: Is this right? smallest prime factor of smaller of amicable pair

Maximilian Hasler maximilian.hasler at gmail.com
Mon Aug 16 19:03:49 CEST 2010

```According to Jan Pederson's web site,
this amicable pair was found by Walker&Einstein in 2001.

Moreover, that web site lists
1673 pairs with members coprime to 30 (193-907 digits),
cf. http://amicable.homepage.dk/apstat.htm#coprime30

Probably the first of them yields the least amicable number with least
prime factor = 7
(and at a first glance there is none with least prime factor > 7).

Maximilian

On Mon, Aug 16, 2010 at 5:43 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> Thank you both, Tony and Charles!  I always like it when a sequence
> that seems stuck in the mud digs its tires out, and climbs onto higher
> ground.
>
> So there should be a comment akin to:
> "The first value other than 2 or 3 was found by Charles Greathouse as
> a(?) = 5480828320492525 = 5^2 * 7^2 * 11 * 13 * 17 * 19 * 23 * 31 * 103 * 1319
>
> On Sun, Aug 15, 2010 at 11:48 PM, Charles Greathouse
> <charles.greathouse at case.edu> wrote:
>> It doesn't hold: 5480828320492525.
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>> On Mon, Aug 16, 2010 at 2:24 AM, T. D. Noe <noe at sspectra.com> wrote:
>>> At 11:14 PM -0700 8/15/10, Jonathan Post wrote:
>>>>2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2,
>>>>2, 2, 2, 2, 2, 2, 3, 2, 2
>>>>smallest prime factor of smaller of amicable pair
>>>>a(n) = A020639(A002025(n)) =   Lpf(A002025(n)) = sigma(A002025(n))-A002025(n).
>>>>Must always be 2 or 3?
>>>
>>>
>>> It is true for all the terms in the b-file for A063990, which includes the
>>> larger of the amicable pair also.
>>>
>>> Tony
>>>
>>>
>>>
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```